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Paper: A class of quadratic APN binomials inequivalent to power functions

Authors:
Lilya Budaghyan
Claude Carlet
Gregor Leander
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URL: http://eprint.iacr.org/2006/445
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Abstract: We exhibit an infinite class of almost perfect nonlinear quadratic binomials from $\mathbb{F}_{2^n}$ to $\mathbb{F}_{2^n}$ ($n\geq 12$, $n$ divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for $n$ even they are CCZ-inequivalent to any known APN function, and in particular for $n=12,24$, they are therefore CCZ-inequivalent to any power function. It is also proven that, except in particular cases, the Gold mappings are CCZ-inequivalent to the Kasami and Welch functions.
BibTeX
@misc{eprint-2006-21936,
  title={A class of quadratic APN binomials inequivalent to power functions},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / Affine equivalence, Almost bent, Almost perfect nonlinear, CCZ-equivalence, Differential uniformity, Nonlinearity, S-box, Vectorial Boolean function},
  url={http://eprint.iacr.org/2006/445},
  note={Part of this paper was presented at ISIT 2006 lilya@science.unitn.it 13482 received 27 Nov 2006, last revised 30 Nov 2006},
  author={Lilya Budaghyan and Claude Carlet and Gregor Leander},
  year=2006
}